Dialog/Recursing
This dialog excerpts a section of the dialog "Verbs," starting at V25 and roughly ending at R48. The topic of "recursing" has broad cultural significance that merits development as this text undergoes subsequent recursive revision (i.e., the topic of "rehearsing" below, V15ff). Over time, the dialogs may form a kind of conceptual latticework as parts of them intersect, appearing in several different dialogs.
On Recursing
V 1 — I've been thinking further about verbs as the source of meaning and understanding, coming back to the matter. The relation between thinking and doing is pretty complicated. When I learned to drive there was a lot that I knew I was supposed to do, but thinking to myself, "use the turn signal," would get me in a muddle because I was also thinking to use the breaks and the steering wheel and each took some conscious attention. It wasn't until I had a little practice that they all fit together easily.
R 2 — Yes. Thinking too much about doing something while trying to do it can seriously impede one's effort. What's going on in the course of that practice? Good coaching helps us develop our awareness of possible adjustments and facilitates our actual incorporating them into our new efforts. We do that through a process of recursion, which arises as we incorporate the results of prior iterations of an action in successive iterations of it. Practice makes perfect through effective recursing, attending to what we are doing and successively incorporating possibilities into what we are doing as we judge them likely to lead to improvement or to avoid complications.
V 3 — OK, I'm beginning to grasp what you are after with all your interest in verbs. The successive instances of a repetitive action become recursive when insight gained from one instance becomes significant in the succeeding instance. We learn by doing as we make what we do recursive. But I had several teachers who would use repetition, drill and practice and memorization as a means of instruction far too much. And my mom keeps trying to have my little sister use a program of math exercises on her tablet that Sis hates because it is so boring.
R 4 — Yeah. For centuries, educators have warned against reliance on repetition and rote learning as instructional methods. But it keeps coming back, usually for the wrong reasons. It's the recursion, not the repetition, that counts. A teacher can tell a kid to repeat something, but he can't very well make the repetition recursive. That's something the kid has to do. A coach can point out a move that would become recursive if the kid incorporates it into his action, but the kid has to do the incorporating, he has to get the feel of it and integrate it into the active flow.
V 5 — The student has to take advantage of repeating something, noticing the effect of variations from one time to the next. For the most part, teachers don't generate or control recursion for others, each student does. A cook who doesn't try her own dishes won't become a master chef. I'm seeing this pretty clearly with that we actually do. Playing basketball, you see someone make a move and think "I could do that" and when the opportunity comes, you try it and mess it up, but sense why, and with a succession of clumsy trials it begins to work, and soon it becomes part of your game.
R 6 — I wish! But even when I could run, I was too short to have much of a game, as you say.
V 7 — Well, I don't quite grasp the importance of thinking the verb that you seem to consider important.
R 8 — Right. I don't think your emulation of someone's basketball move is simply physical. You are there, caught flatfooted for an instant, and there is a spark of recognition — "I could do that" — and you feel what the move consists in and register it, and when you first try and mess it up, you adjust your feel of it mentally, rechoreographing it, and you put that adjusted feel in motion the next time you try. The recursion takes place through your inward processing of the action, consciously and unconsciously, in the interstices between successive occurrences of the action.
V 9 — Doesn't this have something to do with mirror neurons that cognitive scientists talk about?
R 10 — Something. I'm not well versed in cognitive science, but I think a little mystification arises in calling them mirror neurons. I'm pretty sure that what they do differs from the process of reflection that a mirror does even though there is some likeness comparing the results. What do the so-called mirror neurons do? I surmise — mind you, I'm not a researcher and I just reflect on it. . . . — I surmise that these neurons, perhaps other neurons as well, process the initiation and anticipated feedback of different actions without actually carrying the actions out.
V 11 — Are you suggesting that the capacity to process the intellection involved in acting without carrying out the acting enables some sentient creatures to mirror other minds and engage in other forms of feeling and thinking? I can imagine that separation to be significant in many forms of cultural activity.
R 12 — Yes. I suspect the meaning of much of what takes place mentally arises through that separation. Language works as a means to bring it to consciousness. Our ability to direct our attention from one thing to another would suggest we are processing many different kinds of matters at once with them quite disengaged from our acting on them. Sleep seems to shut down many modes of action.
V 13 — Ah! You know how a well designed computer application will give you an indication that it is working when it is doing something slow in the background. I wonder whether fidgeting, a twitch or an itch, are such signals when certain feedback systems are idling with nothing to do.
R 14 — Interesting possibility. Like pinching yourself to make sure you are awake.
V 15 — OK. I'm seeing a little better the relation between thinking a verb and the possibility of recursion. In order to mentally grasp recursive possibilities, we have to be thinking the action of the relevant verb, sensing what we would do to adjust our acting in a fruitful way. As I recurse an action in my own mind, I gain the information and nuance to power recursion. By thinking how we do verbs indicates possibilities we incorporate into the next ... ah! ha! Can we say we rehearse them. We rehearse things, mentally and actively, in order to work on them recursively, uncovering their possibilities and working those into practice.
R 16 — Your jumping from recursing to rehearsing here points to something important. Both have to do with repetition, but the key thing in rehearsing involves repeating or reciting in an interpersonal setting. In some ways, recursing is more open ended than rehearsing. With a good director, the rehearsals of a play might become recursive, extending the script and its interpretation in performance. Recursion takes place when someone uses a function over and over again, each time incorporating possibilities disclosed through its prior activity.
V 17 — OK, outside of special settings like rehearsing a play, does recursion work open-endedly in daily life?
R 18 — When my grand daughter was two she wrapped her fist around a pencil, stabbed a sheet of paper with it, squiggled it around making a weird convoluted line, and looked up, mildly satisfied, and said "Bird." She's now 14 and has sketched many more birds and other things and become quite accomplished, largely self-taught, thinking about how and why the result of a sketch differed from what she wanted it to be and trying to incorporate that understanding into her next effort. She formed her artistic capacities by capturing a lot of feedback from her circumstances, employing it recursively in building up her skills.
V 19 — Yeah. Isn't this a lot like what John Dewey would talk about in Democracy and Education as learning through the reconstruction of experience?
R 20 — Yes, only we are attending more closely to the agent doing the recursing. You know from your computer course that a recursive function needs to be controlled effectively, especially calling it into operation and then terminating it at the right time in the right way. There is a big difference between programming the computer and living in the world, however. In the one you control the recursing for the computer, in the other your control it for yourself.
V 21 — Er.... Let me see if I really understand your point with respect to A Place to Study. I'm beginning to see that it's pretty radical. You're suggesting that in formal instruction it's difficult to make use of recursing because calling an action into operation, getting attention latched onto it through its operation, and then deciding when to stop it and moving onto something else is not really in the control of the teacher and the formal curriculum. Is that what your are suggesting?
R 22 — Yes. What does didactic thinking obsess over — arousing interest and maintaining attention in a group of persons. As sentient, living persons embodied in ourselves and the world around us, we cannot turn over to another full control of our awareness and concentration, our interest and attention. Now make no mistake. I don't think we can or should give up our systems of instruction, but in addition to those we can and should support a freer form of self-education, one that I think can capture the power of recursive self-development more effectively.